1. Field of the Invention
The present invention relates to a warpage of a multilayered substrate in implementation of electronic equipment. More specifically, controlling a warpage of a multilayered substrate in which different materials—a resin substrate material and a wiring material—are distributed two-dimensionally in an upper wiring layer and a lower wiring layer.
2. Description of Related Art
In implementation of electronic equipment, there is a problem of a warpage of a multilayered substrate or package. A warpage of a multilayered organic substrate occurs primarily because of asymmetry of the coefficient of thermal expansion (CTE) between upper and lower wiring layers thereof.
In the upper and lower wiring layers of the multilayered organic substrate, different materials—a resin substrate material and a wiring material—are distributed two-dimensionally.
The resin substrate material is typically an insulating resin, and the wiring material is typically a conductive metal. Therefore, these materials have significantly different coefficients of thermal expansion and elastic moduli, or elasticity, E.
When the wiring material is distributed in the resin substrate material, the wiring material cannot be, inherently, of perfect geometric symmetry, and therefore the distribution of the wiring material is asymmetric. In this respect, there is a demand for a method of optimizing wiring.
According to a known approach to reduce a warpage, a dummy pattern is formed so that the upper and lower wiring layers of the substrate have equal wiring densities. However, at present, there is no way to numerically determine which part should be preferentially corrected in wiring density, and technicians have to empirically or intuitively make the determination.
As a known second best solution, there is a concept of determining an average coefficient of thermal expansion, which is an average of the coefficients of thermal expansion of the upper and lower wiring layers. According to this concept, a warpage of a substrate is analyzed by adjusting the wiring pattern so that the density of the wiring layers is uniform over the whole of the substrate. However, the difference in coefficient of thermal expansion can partially or locally increase, or some wiring patterns cannot be modified for convenience of wiring.
At present, even a partial or local modification of the wiring pattern is usually empirically or intuitively made by the designer of the wiring pattern.
Japanese Patent No. 4204530 describes an FEM analysis that involves dividing an area, in which precise calculation of the warpage is needed, into a fine mesh of elements and dividing an area, in which precise calculation of the warpage is not needed into a coarse mesh of elements.
Japanese Patent No. 3329667 describes a method of determining the position of a reinforcing member with respect to a warpage of a printed circuit board.
PCT Application Publication No. WO 2010/021287 describes a warpage prediction program based on the finite element method (FEM).
Japanese Patent No. 4204524 and Japanese Application Publication Nos. 2012-3460, 2001-14865, 2010-118523, 2010-87145, 2009-260123 describe analyses of a warpage of a substrate based on the finite element method, which can be used for reference purposes.
However, no technique has been found that focuses on variations of the difference in average coefficient of thermal expansion Δα in a substrate and is based on, and applies to a correction, a concept of distinguishing between the difference in coefficient of thermal expansion Δα with a greater length scale (a lower frequency) that has a significant effect on the warpage and the difference in coefficient of thermal expansion Δα with a smaller length scale (a higher frequency) that has a less significant effect on the warpage.